Fibred surfaces and moduli (Q1196415)

The author studies surjective morphisms \(\varphi:S\to C\) with connected fibers from a smooth projective surface \(S\) onto a smooth curve \(C\). He proves a criterion for isotriviality, i.e. constant isomorphism type of the fibers of \(\varphi\), in terms of the number of sections of tensor powers of the relative canonical sheaf of \(\varphi\). Furthermore generalizing a result of \textit{F. Catanese} [Invent. Math. 104, No. 2, 263-289 (1991; Zbl 0743.32025)] he gives a bound for the dimension of \(H^ 1(S,T_ S)\) for an arbitrary nonisotrivial \(\varphi\).